The present disclosure relates generally to an extremum-seeking control (ESC) system. ESC is a class of self-optimizing control strategies that can dynamically search for the unknown and/or time-varying inputs of a system for optimizing a certain performance index. ESC can be considered a dynamic realization of gradient searching through the use of dither signals. The gradient of the system output y with respect to the system input u can be obtained by slightly perturbing the system operation and applying a demodulation measure. Optimization of system performance can be obtained by driving the gradient towards zero by using a negative feedback loop in the closed-loop system. ESC is a non-model based control strategy, meaning that a model for the controlled system is not necessary for ESC to optimize the system.
ESC typically involves online estimation of a property related to the gradient of a cost function relative to a manipulated variable. The manipulated variable can be continuously adjusted in order to move to a point where this gradient measure is zero. It is straightforward to apply constraints to the variable being manipulated by using upper and lower bounds. However, it may be desirable to also constrain other variables that are affected by the operation of ESC within certain bounds. The problem of applying constraints to other variables affected by ESC can be difficult to handle within the ESC framework.